Open Access
April 2018 Multiscale blind source separation
Merle Behr, Chris Holmes, Axel Munk
Ann. Statist. 46(2): 711-744 (April 2018). DOI: 10.1214/17-AOS1565


We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an $\varepsilon$-neighborhood of the mixture when the sources take only values in a known finite alphabet. Based on this we provide the SLAM (Separates Linear Alphabet Mixtures) estimators for the mixing weights and sources. For Gaussian error, we obtain uniform confidence sets and optimal rates (up to log-factors) for all quantities. SLAM is efficiently computed as a nonconvex optimization problem by a dynamic program tailored to the finite alphabet assumption. Its performance is investigated in a simulation study. Finally, it is applied to assign copy-number aberrations from genetic sequencing data to different clones and to estimate their proportions.


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Merle Behr. Chris Holmes. Axel Munk. "Multiscale blind source separation." Ann. Statist. 46 (2) 711 - 744, April 2018.


Received: 1 July 2016; Revised: 1 January 2017; Published: April 2018
First available in Project Euclid: 3 April 2018

zbMATH: 06870277
MathSciNet: MR3782382
Digital Object Identifier: 10.1214/17-AOS1565

Primary: 62G08 , 62G15
Secondary: 92D10

Keywords: change point regression , exact recovery , finite alphabet linear mixture , genetic sequencing , honest confidence sets , multiscale inference

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.46 • No. 2 • April 2018
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